Hodges-Lehmann Optimality for Testing Moment Conditions

Author(s):  
Ivan A Canay ◽  
Taisuke Otsu
Keyword(s):  
2000 ◽  
Vol 23 (11) ◽  
pp. 789-794 ◽  
Author(s):  
Soo Hak Sung

Let{Xni}be an array of rowwise independentB-valued random elements and{an}constants such that0<an↑∞. Under some moment conditions for the array, it is shown that∑i=1nXni/anconverges to0completely if and only if∑i=1nXni/anconverges to0in probability.


2014 ◽  
Vol 32 (1) ◽  
pp. 30-70 ◽  
Author(s):  
Xiaohong Chen ◽  
David T. Jacho-Chávez ◽  
Oliver Linton

We establish the consistency and asymptotic normality for a class of estimators that are linear combinations of a set of$\sqrt n$-consistent nonlinear estimators whose cardinality increases with sample size. The method can be compared with the usual approaches of combining the moment conditions (GMM) and combining the instruments (IV), and achieves similar objectives of aggregating the available information. One advantage of aggregating the estimators rather than the moment conditions is that it yields robustness to certain types of parameter heterogeneity in the sense that it delivers consistent estimates of the mean effect in that case. We discuss the question of optimal weighting of the estimators.


2016 ◽  
Vol 93 (3) ◽  
pp. 248-250 ◽  
Author(s):  
F. Götze ◽  
A. A. Naumov ◽  
A. N. Tikhomirov ◽  
D. A. Timushev

2009 ◽  
Vol 25 (2) ◽  
pp. 482-526 ◽  
Author(s):  
Tassos Magdalinos ◽  
Peter C.B. Phillips

An asymptotic theory is developed for multivariate regression in cointegrated systems whose variables are moderately integrated or moderately explosive in the sense that they have autoregressive roots of the form ρni = 1 + ci/nα, involving moderate deviations from unity when α ∈ (0, 1) and ci ∈ ℝ are constant parameters. When the data are moderately integrated in the stationary direction (with ci < 0), it is shown that least squares regression is consistent and asymptotically normal but suffers from significant bias, related to simultaneous equations bias. In the moderately explosive case (where ci > 0) the limit theory is mixed normal with Cauchy-type tail behavior, and the rate of convergence is explosive, as in the case of a moderately explosive scalar autoregression (Phillips and Magdalinos, 2007, Journal of Econometrics 136, 115–130). Moreover, the limit theory applies without any distributional assumptions and for weakly dependent errors under conventional moment conditions, so an invariance principle holds, unlike the well-known case of an explosive autoregression. This theory validates inference in cointegrating regression with mildly explosive regressors. The special case in which the regressors themselves have a common explosive component is also considered.


2008 ◽  
Vol 24 (5) ◽  
pp. 1456-1460 ◽  
Author(s):  
Hailong Qian

In this note, based on the generalized method of moments (GMM) interpretation of the usual ordinary least squares (OLS) and feasible generalized least squares (FGLS) estimators of seemingly unrelated regressions (SUR) models, we show that the OLS estimator is asymptotically as efficient as the FGLS estimator if and only if the cross-equation orthogonality condition is redundant given the within-equation orthogonality condition. Using the condition for redundancy of moment conditions of Breusch, Qian, Schmidt, and Wyhowski (1999, Journal of Econometrics 99, 89–111), we then derive the necessary and sufficient condition for the equal asymptotic efficiency of the OLS and FGLS estimators of SUR models. We also provide several useful sufficient conditions for the equal asymptotic efficiency of OLS and FGLS estimators that can be interpreted as various mixings of the two famous sufficient conditions of Zellner (1962, Journal of the American Statistical Association 57, 348–368).


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